Simplifying
by combining like terms -4b-3a+2c+3b-5

Answer:

C

Step-by-step explanation:

f(x) • g(x)

= \(\sqrt{x^2+12x+36}\) × (x³ - 12)

= \(\sqrt{(x+6)^2}\) × (x³ - 12)

= (x + 6)(x³ - 12)

= x(x³ - 12) + 6(x³ - 12) ← distribute parenthesis

= \(x^{4}\) - 12x + 6x³ - 72

= \(x^{4}\) + 6x³ - 12x - 72

Answer:

See photo

Step-by-step explanation:

Plato/Edmentum

Answer:

9375

Step-by-step explanation:

Answer:

x = 53

Step-by-step explanation:

The angle labeled with the expression "2x - 20 " and the angle with the measure of 86 degrees are opposite interior angles.

Opposite interior angles are congruent

This means that 2x - 20 = 86

This is our equation.

We now solve for x using basic algebra

2x - 20 = 86

step 1 add 20 to each side

-20 + 20 cancels out

86 + 20 = 106

now we have 2x = 106

step 2 divide each side by 2

2x / 2 = x

106 / 2 = 53

we're left with x = 53

Answer:

\(8 \pi\)

Step-by-step explanation:

The computation of the volume of water remaining is shown below:

The volume of the cone is

\(\pi r^2 \frac{h}{3}\\\\\pi \times 3^2 \times \frac{8}{3} \\\\\frac{72}{3} \pi \\\\24 \pi\)

Now since it is two-third so the remaining is one -third

\(= 24 \pi \times \frac{1}{3}\)

\(= 8 \pi\)

hence, the volume of water remaining is \(8 \pi\)

Shawn's first statement is correct. A trapezoid is a quadrilateral with at least one pair of parallel sides. A rectangle is a quadrilateral with four right angles and opposite sides of equal length. It is not possible to draw a trapezoid that is a rectangle, because the two shapes have different sets of properties.

However, Shawn's second statement is incorrect. A square is a type of rectangle in which all sides are of equal length. So, every square is a rectangle, but not every rectangle is a square. So it is not accurate to say that it is possible to draw a square that is a rectangle, because a square is already a type of rectangle.

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No, the independence of x and y does not necessarily mean the independence of \(x^2\) and y.

Independence means that the values of one random variable do not affect the values of the other random variable. In other words, knowing the value of one random variable does not give us any information about the value of the other random variable.

However, squaring a random variable changes its distribution and can affect its independence from another random variable.

For example, if x is a normally distributed random variable with a mean of 0 and a standard deviation of 1, then \(x^2\) will follow a chi-squared distribution with 1 degree of freedom. The distribution of \(x^2\) and y may not be independent, even though x and y are independent.

Hence, just because x and y are independent random variables does not mean that  \(x^2\)  and y are also independent random variables. Independence must be established based on the joint distribution of the random variables.

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Answer:

slope of AB = 0

Step-by-step explanation:

The slope of the x- axis OX = 0

Since AB is parallel to the x- axis and parallel lines have equal slopes, then

slope of AB = 0

Since, the line AB is parallel to X - axes, so every point on the the line AB will have equal Y - coordinates.

lets take it as Y ( y - coordinate is same )

slope :

=》

\( \dfrac{y2 - y1}{x2 - x1} \)

but since y2 and y1 are equal, so

\( \dfrac{ Y - Y }{x2 - x1} \)

=》

\( \dfrac{0}{x2 - x1} \)

=》

\(0\)

Answer:

15 m

Step-by-step explanation:

Height of buiding h= 9m

Lenght from building l= 12m

let the length of the rope be x=???

Applying Pythagoras theorem

x^2=h^2+l^2

x^2= 9^2+12^2

x^2= 81+144

x^2=225

square both sides

x=√225

x=15 m

Hence the length of the rope is 15 m

In a primitive Pythagorean triple, the sides a, b, and c are all integers, and they satisfy the equation a^2 + b^2 = c^2.

Now, let's assume that neither x nor y is divisible by 3. This means that x and y can only be 1, 2, 4, 5, 7, or 8 modulo 3. Therefore, x^2 and y^2 can only be 1 or 4 modulo 3. Now, let's consider the equation a^2 + b^2 = c^2 mod 3. If a and b are both 1 or both 2 modulo 3, then their squares will add up to 2 modulo 3, which is not a quadratic residue. Therefore, one of a and b must be 0 modulo 3, and hence, c must also be divisible by 3. We assumed that neither x nor y is divisible by 3. We then looked at the possible residues of x and y modulo 3 and saw that they can only be 1, 2, 4, 5, 7, or 8 modulo 3. We then used the fact that the sum of two quadratic residues is not a quadratic residue modulo 3, and concluded that one of a and b in the Pythagorean triple must be divisible by 3.

In conclusion, either x or y in a primitive Pythagorean triple must be divisible by 3. This is a result of the fact that the sum of two quadratic residues is not a quadratic residue modulo 3.

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Answer:

probability for 3 on a dice (P3) in one dice =

\( \frac{1}{6} \)

probability for even no. of a dice (Pe) =

\( \frac{3}{6} = \frac{1}{2} \)

Therefore, the probability of finding 3 on one dice and even on another (P) = P3 + Pe

\( = \frac{1}{6} + \frac{1}{2} = \frac{1 + 3}{6} = \frac{4}{6} = \frac{2}{3} \)

Answer:

45 - 25 = 20 / 10 = 2 meaning he used the boat for 2 hours.

Step-by-step explanation:

Its the same this as before you start by writing it out how the way PEMDAS works. PEMDAS is ( Parenthesis, Exponents, Multiplication, Division, Adding, and Subtraction). Also i accidentally messed up my other answer so give me a sec.

To evaluate the given integrals using polar coordinates, from Cartesian coordinates to polar coordinates. In each case, given regions or curves in polar form and apply the appropriate limits of integration to compute the integral.

7. To evaluate the integral ∫∫R x dA, where R is the top half of the disk with center at the origin and radius r, we convert to polar coordinates. In polar form, the region R is defined by 0 ≤ r ≤ r and 0 ≤ θ ≤ π. The integral becomes ∫∫R x dA = ∫₀ʳ ∫₀ᴨ x r dr dθ. Evaluating this integral gives the desired result.

8. The integral ∫∫R x dA, where R is the region in the first quadrant enclosed by the circle x² + y² = r² and the lines y = x and x = 0, can be evaluated using polar coordinates. Converting the equations to polar form gives r² = r²cos²θ + r²sin²θ and θ = π/4 and θ = 0 as the limits of integration. The integral becomes ∫∫R x dA = ∫₀ʳ ∫₀ᴨ/₄ x r dr dθ. Evaluating this integral gives the desired result.

9. The integral ∫∫R x dA, where R is the region in the first quadrant between the circles x² + y² = a² and x² + y² = b² (where a < b), can be evaluated using polar coordinates. In polar form, the region R is defined by a ≤ r ≤ b and 0 ≤ θ ≤ π/2. The integral becomes ∫∫R x dA = ∫ₐᵇ ∫₀ᴨ/₂ x r dr dθ. Evaluating this integral gives the desired result.

10. The integral ∫∫R x dA, where R is the region that lies between the circles x² + y² = a² and x² + y² = b² (where a < b), can be evaluated using polar coordinates. In polar form, the region R is defined by a ≤ r ≤ b and 0 ≤ θ ≤ 2π. The integral becomes ∫∫R x dA = ∫ₐᵇ ∫₀²ᴨ x r dr dθ. Evaluating this integral gives the desired result.

11. The integral ∫∫R x dA, where R is the region bounded by the semi-circle x = √(r² - y²) and the x-axis, can be evaluated using polar coordinates. Converting the equations to polar form gives r = rcosθ and θ = -π/2 and θ = π/2 as the limits of integration. The integral becomes ∫∫R x dA = ∫₋ᴨ/₂ᴨ/₂ ∫₀ʳ x r dr dθ. Evaluating this integral gives the desired result.

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option C, which shows a line graph, is the appropriate graph that Josie can use to help her budget.

What is the linear function?

A linear function is defined as a function that has either one or two variables without exponents. It is a function that graphs to a straight line.

Josie can use a line graph to help her budget since the given function is a linear function.

The graph of a linear function is a straight line, and a line graph is a graph that represents data with points connected by straight lines.

Therefore, option C, which shows a line graph, is the appropriate graph that Josie can use to help her budget.

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Complete question:
The graphs are in the attached image.

Answer:

y=3x

Step-by-step explanation:

Therefore, the maximum blood pressure of 200 mmHg occurs at approximately 0.524 seconds, and the minimum blood pressure of 120 mmHg occurs at approximately 1.571 seconds within the time interval 0 ≤ t ≤ 0.75.

To find the maximum and minimum values of the blood pressure function p(t), we need to examine the behavior of the sinusoidal term, -40sin(3t), within the given time interval. The function is a sine wave with an amplitude of 40 and a period of 2π/3. This means that the maximum value occurs at the peak of the sine wave (amplitude + offset), and the minimum value occurs at the trough (amplitude - offset).

The maximum blood pressure corresponds to the peak of the sine wave, which is 40 + 160 = 200 mmHg. To find the time at which this occurs, we set the argument of the sine function, 3t, equal to π/2 (since the peak of the sine wave is π/2 radians). Solving for t gives t = (π/2) / 3 = π/6 ≈ 0.524 seconds.

Similarly, the minimum blood pressure corresponds to the trough of the sine wave, which is -40 + 160 = 120 mmHg. Setting the argument of the sine function equal to 3π/2 (the trough of the sine wave), we find t = (3π/2) / 3 = π/2 ≈ 1.571 seconds.

Therefore, the maximum blood pressure of 200 mmHg occurs at approximately 0.524 seconds, and the minimum blood pressure of 120 mmHg occurs at approximately 1.571 seconds within the time interval 0 ≤ t ≤ 0.75.

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Answer:

Was the question meant to say "what is the value of 4x-7 when x=4?" if so the answer is 9.

Step-by-step explanation:

First plug in 4 for x. The equation should then read 4(4) -7

Next use pemdas to solve (multiple 4 × 4 and then subtract 7 to get the answer 9

Answer:

9/2 or 4 1/2

Step-by-step explanation:

So let's break this up...

We need to flip the right-hand side of the division sign upside down and then change the division sign to a multiplication sign.

So the equation will now look like this -3 * (-3/2) which is 9/2 or 4 1/2

Hope this helps!

Answer:

9/2

Step-by-step explanation:

# mark above answer Brilliantly

here for just POINTS

thanks for POINTS ..

Answer:

it needed your to focus on school work , homework and work hard to make yourself feel ready

The equation relating x, y, and z is:

z = 0.5 * x * y.

In the given problem, the relationship between x, y, and z can be expressed by the equation z = k * x * y, where k represents the constant of proportionality. By substituting the values of x = 4 and y = 5, when z is equal to 10, we can determine the value of the constant of proportionality, k, and further define the relationship between the variables.

To find the constant of proportionality, we substitute the known values of x = 4, y = 5, and z = 10 into the equation z = k * x * y. This gives us the equation 10 = k * 4 * 5. By simplifying the equation, we have 10 = 20k. To isolate k, we divide both sides of the equation by 20, resulting in k = 0.5. Therefore, the equation relating x, y, and z is z = 0.5 * x * y, meaning that z is directly proportional to the product of x and y with a constant of proportionality equal to 0.5.

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Answer:

download a calculator

Step-by-step explanation:

Let \(\(a\)\) and \(\(b\)\) be integers such that \(\(ab = 4\)\). We want to prove that \(\((a - b)^3 - 9(a - b) = 0\).\)

Starting with the left side of the equation, we have:

\(\((a - b)^3 - 9(a - b)\)\)

Using the identity \(\((x - y)^3 = x^3 - 3x^2y + 3xy^2 - y^3\)\), we can expand the cube of the binomial \((a - b)\):

\(\(a^3 - 3a^2b + 3ab^2 - b^3 - 9(a - b)\)\)

Rearranging the terms, we have:

\(\(a^3 - b^3 - 3a^2b + 3ab^2 - 9a + 9b\)\)

Since \(\(ab = 4\)\), we can substitute \(\(4\)\) for \(\(ab\)\) in the equation:

\(\(a^3 - b^3 - 3a^2(4) + 3a(4^2) - 9a + 9b\)\)

Simplifying further, we get:

\(\(a^3 - b^3 - 12a^2 + 48a - 9a + 9b\)\)

Now, notice that \(\(a^3 - b^3\)\) can be factored as \(\((a - b)(a^2 + ab + b^2)\):\)

\(\((a - b)(a^2 + ab + b^2) - 12a^2 + 48a - 9a + 9b\)\)

Since \(\(ab = 4\)\), we can substitute \(\(4\)\) for \(\(ab\)\) in the equation:

\(\((a - b)(a^2 + 4 + b^2) - 12a^2 + 48a - 9a + 9b\)\)

Simplifying further, we get:

\(\((a - b)(a^2 + 4 + b^2) - 12a^2 + 39a + 9b\)\)

Now, we can observe that \(\(a^2 + 4 + b^2\)\) is always greater than or equal to \(\(0\)\) since it involves the sum of squares, which is non-negative.

Therefore, \(\((a - b)(a^2 + 4 + b^2) - 12a^2 + 39a + 9b\)\) will be equal to \(\(0\)\) if and only if \(\(a - b = 0\)\) since the expression \(\((a - b)(a^2 + 4 + b^2)\)\) will be equal to \(\(0\)\) only when \(\(a - b = 0\).\)

Hence, we have proved that if \(\(ab = 4\)\), then \(\((a - b)^3 - 9(a - b) = 0\).\)

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Approximately 30.79% of trucks can be expected to travel less than 15,000 or more than 40,000 miles per year.

To determine the percentage of trucks that can be expected to travel either less than 15 or more than 40 thousand miles in a year, we can use the properties of the normal distribution.

Let's calculate the z-scores for 15,000 miles and 40,000 miles using the given mean and standard deviation:

For 15,000 miles:

z-score = (x - mean) / standard deviation

= (15,000 - 30,000) / 12,000

= -15,000 / 12,000

= -1.25

For 40,000 miles:

z-score = (x - mean) / standard deviation

= (40,000 - 30,000) / 12,000

= 10,000 / 12,000

= 0.8333

Now, we can use a z-table or a statistical calculator to find the percentage of trucks that fall below -1.25 or above 0.8333 in terms of z-scores.

From the z-table or calculator, we find the following probabilities:

For a z-score of -1.25, the corresponding probability is approximately 0.1056 or 10.56%.

For a z-score of 0.8333, the corresponding probability is approximately 0.7977 or 79.77%.

To find the percentage of trucks that travel either less than 15,000 or more than 40,000 miles in a year, we add the probabilities together:

10.56% + (100% - 79.77%) = 10.56% + 20.23% = 30.79%

Therefore, approximately 30.79% of trucks can be expected to travel either less than 15,000 or more than 40,000 miles in a year.

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ANSWER: 100

EXPLANATION: Based on the given conditions, formulate:: 70 + 6 x 5

Calculate the product or quotient: 70 + 30

Calculate the sum or difference: 100

The savings made by Chee after six weeks will be $100.

Given is that Chee is saving up to buy a new phone. She already has $70 and can save an additional $5 per week using money from her after school job.

We can write that after [w] weeks of savings, the expression for the total money can be written as -

C(w) = 70 + 5w

For [w] = 6 weeks, we can write -

C(6) = 70 + 5 x 6 = 100

Therefore, the total savings made by Chee after six weeks will be $100.

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Answer:

the answer is that the money is a function

Step-by-step explanation:

Answer:

a. Yes because each input value has the same output value.

b. Yes the relationship is linear because if you were to graph the information you would get a straight line.

Step-by-step explanation:

I'm not very good at explaining my reasoning haha but I hope this works :)

Answer:

B. Non-negative real number

Step-by-step explanation:

For a complex number, multiplying by the conjugate always gives Non-negative real number

Anaiah currently spending  $150 on these goods

*He is not spending his entire income  

*His marginal utility per dollar spent is not the same for both goods

What is unit rate?

A unit rate is the cost for only one of anything. This is expressed as a ratio with a denominator of 1. For instance, if you covered 70 yards in 10 seconds, you did so at an average speed of 7 yards per second. Although both of the ratios—70 yards in 10 seconds and 7 yards in one second—are rates, only the latter is a unit rate.

consumption of eggplant

= 20 price of eggplant

= 3

consumption of kiwi is

= 30 price of eggplant

= 3

Formula:

Spending

= price of eggplant*consumption of eggplant + price of kiwi*consumption of kiwi

= 3*20+3*30

= 150

Utility per one dollar spent on the 20th eggplant

=  160

Marginal utility per dollar spent on the 30th kiwi

= 190 utils.

Note that y 160<190

Currently spending= 150

& budget = 180

150<180

According theory of choice consumer need the maximize the utility so answer is

Answer -:

*He is not spending his entire income

*His marginal utility per dollar spent is not the same for both goods

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Step-by-step explanation:

you did not find the formulas on the internet and/or don't have a calculator ?

the volume of any regular 3D object is

base area × height

so, the volume of the triangular prism is

triangle area × 10

a triangle area is

baseline × inner height / 2

and if I see this right, the triangle is right-angled. so the legs enclosing the 90° angle can be seen as baseline and inner height.

so, for the volume again, we get

baseline × inner height /2 × height = 3×8 /2 × 10 =

= 24 × 5 = 120 units³

the volume of a cone is

pi×r²×height/3

so, in our case

pi×5²×6/3 = pi×25×2 = 50pi = 157.0796327... units³

the volume of a cylinder is again base area ×height

pi×r²×height

so, in our case

pi×5²×8 = pi×25×8 = 200pi = 628.3185307... units³

the volume of a pyramid is

length×width × height / 3

so, in our case

3×4 × 6 / 3 = 12 × 2 = 24 units³